First-principles calculation of 11B solid-state NMR parameters of boron-rich compounds I: the rhombohedral boron modifications and B12X2 (X = P, As, O)

Abstract

In the present study, solid-state nuclear magnetic resonance (NMR) spectra under magic angle spinning conditions of the rhombohedral structures α-B and B₁₂P₂ are reported together with the corresponding parameter sets from first principles calculations on α-B B₁₂X₂ (X = P, As, O). With the combination of density functional theory (DFT) and the gauge-including projector-augmented wave (GIPAW) approach as the theoretical tools at hand the computed ¹¹B parameters lead to unambiguous explanation of the measurements. Thereby, we overcome common obstacles of processing recorded NMR spectra of solid-state compounds with several crystallographic positions, in particular non-trivial signal assignments and parameter determination due to peak overlap or even unexpected intensity/area ratios. In fact, we find very good agreement between the theoretical results and measured spectra without applying fitting procedures. Using the Perdew–Burke–Ernzerhof (PBE) functional, the results of the common construction types for pseudopotentials and referencing methods for the chemical shift determination are compared. Suggestions and conclusions from experimental ¹¹B NMR studies on parameters according to the icosahedral positions are critically discussed, for instance the early suspected correlation to chemical shifts is not confirmed. Regarding the electric field gradient (EFG) a detailed explanation for obtaining small deviations amongst all investigated structures of the icosahedral polar sites compared to the equatorial sites is given. Our results show an important link between the exohedral bonding situation of compounds with icosahedral structure elements and the main axis of the EFG and therefore, also measurable quadrupole coupling constants if certain geometrical conditions are fulfilled. Finally, this work also contributes to establishing the number of unique sites measured by solid-state NMR methods within the modification of β-B.